How to add/simplify rational expressions

Question

How do I add and simplify this rational expression step by step?? 

 

 

  7     +     x+30    

x+2          x^2_4

Answer 1

1. Expand x² - 4.  This gives you (x + 2)(x - 2)

 

Now you have

    (7)     +      x + 30       

  x + 2         (x + 2)(x - 2)   

 

 

2. Find a common denominator between (x + 2) and (x + 2)(x - 2)

 

This means that both denominators have to be (x + 2)(x - 2)

 

 

3. In order to get the denominators to be the same, the front fraction has to be multiplied by (x - 2) on top and bottom.

 

      7(x - 2)       

  (x + 2)(x - 2)

 

4. Add the fractions together

   7x - 14 + x + 30

   8x + 16

 

5. Reduce

    8x + 16       

  (x + 2)(x - 2)

 

  8(x + 2)

(x + 2)(x - 2)

 

6. Cross out the factor that is common in top and bottom and you have your answer.